There is apparently some confusion about trademarks in PP circles.
Are trademarks basically OK? Yes and no.
Trademarks essentially protect vendor reputations. Which makes them a useful alternative even for patents: it allows competitive products, but not under the guise of someone else.
Still, there is a number of problems with trademarks:

Exhaustion

There used to be worldwide exhaustion, until about 20 years ago. In US terminology, this is the „first sale doctrine“: once a product is sold, one is free to resell it, using the trademark. Under the present regime, people were prosecuted for offering second hand products on eBay, mentioning the trademark. Within EU, that is allowed. Selling e.g. a product bought in the US in EU is illegal if the trademark is used. Which is obviously preposterous in the Internet era. Vendors may claim that they don't want prople to buy 2nd hand products, because it decreases their profits, and it may hurt the luxury image of products.

Criminalization

Perhaps there is a reason to criminalize outright fake products (same products with a trademark that mimics the original as closely as possible). But there is also trademark infringement if a trademarks only resembles a protected trademark too closely. What is „too closely“? The ECJ defined the „confusion“ criterion in the Puma v. Sahel case (for Germans known as „springende Raubkatze“). This requires a very subtle judgment, certainly beyond the competence of criminal authorities, let alone customs. Similarly, „dilution“ or any other action that hurts the reputation or distinctive quality of a trademark may be illegal. That is not something to criminalize either.

Accumulation

Some PPs object the accumulation of copyright and trademarks. I don't think it can be prevented, and I don't think it is a specific problem. Any original text, drawing, 3-D shapes etc. gets copyright protection automatically by law. And obviously these „signs“ are used as trademarks. Obviously, abuse should be prevented. Like the smart Dutch publisher who tried to (effectively) extend the copyright of the (locally) famous „Dick Trom“ books after it expired by registering the title and cover as trademarks.

Scope of protection

Trademark are registered for certain classes. Which allows a trademark to be reused in a (very) different field of endeavor. For instance, Ajax is not only a famous Dutch football club, but also the trademark of fire extinguishers, and a detergent. So far so good. But trademark owners may also abuse their trademarks. Example: the „ICE“ trademark of German high-speed trains is also registered for travel bags. Here the trademark is not used to protect a product, but only to make money.

Parallel import

Trademarks prevent parallel import, outside the EU. Reasons for vendors to prevent parallel import include: price protection, protection of (luxury) brand image, serviceability of products (including the „problem“ of non-authorized dealers and repair shops, e.g. for cars). Perhaps some of these reason are valid, but consumers are faced with higher prices if parallel imports are prohibited. Within EU, luxury perfume seller Dior tried to resort to copyright - by default of trademark protection within EU preventing reselling - to prevent discount drugstore chain Evora (owner of Kruidvat, well-known in NL) to advertise using images of the their bottles - because that would hurt the luxury image of their brand. The court did not accept the argument (Google: Dior-Evora).

Bad faith trademark registration

Legal enforceability of trademarks depends on registration. Traders may have forgotten to register the trademark they are using, which allows a competitor to register the trademark, end prevent the original user from using it. PP should oppose that (but it is current law).

Dilution

Vendors often like their brand name to be considered a synonym for the product, because it gives the impression that the product is the only one. For instance, „powerpoint“ is often used as a synonym for: PC-based presentation. „Oh no, I prefer Open Office 'Impress' as my powerpoint tool“. Somehow contradictory, it may be illegal to use a brand name in such a way that it causes the trademark to loose its distinctive quality! Because a trademark may be no longer be considered enforceable if it really deteriorated to a species name. For instance, it may be illegal to designate a certain type of train as „intercity“, because it is a registered trademark! Obviously, such „abuse“ of trademarks should not be prosecuted.

Customs

The ownership of trademark-infringing products for personal use is not considered illegal (at least in NL), but importing is. Afaik customs authorities are not actively prosecuting travelers importing infringing products. But one day that may change. Would I be caught wearing the 10 euro Rolex watch I bought on the market in Bangkok? Or using the 15 euro „North Face“ backpack I bought in Saigon?

Incidentally, there are rumors that Lacoste manufactures the (alleged) illegal fakes sold on Asian markets themselves! (which can be proven by chemical analysis of the dyes that are used)

In sum. trademarks are not really innocent. Yes, they may provide a better alternative for patents. But e.g. criminalization of trademark infringement is definitely a risk.